Electrically small antennas have a maximum dimension that is relatively small compared to the electrical wavelength, and have attracted attention in recent years largely for this reason. Applications include mobile phones, UHF, VHF, and lower frequency radio applications (where most practical antennas are compact), and microwave applications where miniaturization may be desirable.
In some applications, such as a multi-band radio, broadband performance is desirable, which is correlated to having a low quality factor (Q) value. The Chu limit defines a minimum achievable Q for a given size and wavelength of operation:
                              Q          min                =                  (                                    1                                                (                  ka                  )                                3                                      +                          1                              (                ka                )                                              )                                    (        1        )            where k is the wavenumber of the radiation (2π/wavelength) and α is the radius of an imaginary sphere that just encloses the antenna. Thus, it can be desirable to find antenna designs that approach the Chu limit. The hemispherical helix antenna is one such design, which has been demonstrated to achieve a Q of 1.5 times the Chu limit. FIG. 9, discussed further below, illustrates a four-arm hemispherical helix antenna in which each arm is integrally formed from a solid piece of wire.
However, the structure of a solid wire hemispherical helix presents a fabrication challenge in order to realize the designed geometry in a timely and inexpensive fashion. Accordingly, there remains ample opportunity for improved structures and design and manufacturing processes for three dimensional antennas.